22k+2k^2=13

Solution for 22k+2k^2=13 equation:

22k+2k^2=13

We move all terms to the left:

22k+2k^2-(13)=0

a = 2; b = 22; c = -13;
Δ = b2-4ac
Δ = 222-4·2·(-13)
Δ = 588
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-14\sqrt{3}}{2*2}=\frac{-22-14\sqrt{3}}{4}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+14\sqrt{3}}{2*2}=\frac{-22+14\sqrt{3}}{4}
$